Load libraries

library(tidyverse) # data manipulation
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## ✔ lubridate 1.9.2     ✔ tidyr     1.3.1
## ✔ purrr     1.0.2     
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library(ggpubr) # producing data exploratory plots
library(modelsummary) # descriptive data 
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library(glmmTMB) # running generalised mixed models 
library(DHARMa) # model diagnostics 
## This is DHARMa 0.4.6. For overview type '?DHARMa'. For recent changes, type news(package = 'DHARMa')
library(performance) # model diagnostics  
library(ggeffects) # partial effect plots 
library(car) # running Anova on model
## Loading required package: carData
## 
## Attaching package: 'car'
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Import data

df_adults <- read_csv("resp_results_adults.csv")
df_jresp <- read_csv("resp_results_juveniles.csv")

Data manipulation

Adults

df_adults_cleaned <- df_adults |> 
  mutate(FISH_ID = factor(FISH_ID), 
         Sex = factor(Sex), 
         Population = factor(Population), 
         Tank = factor(Tank), 
         Chamber = factor(Chamber), 
         System =factor(System), 
         Temperature =factor(Temperature), 
         True_resting=factor(True_resting)) 

df_males <- df_adults_cleaned |> 
  filter(Sex == "M")
df_females <- df_adults_cleaned |> 
  filter(Sex == "F")

df_adults_cleaned2 <- df_males |> 
  full_join(select(df_females, c("Tank","Temperature","Mass","Resting","Max","AAS","FISH_ID","Sex")), by="Tank") |> 
  mutate(Temperature.x = coalesce(Temperature.x, Temperature.y), 
         FISH_ID.x = coalesce(FISH_ID.x, FISH_ID.y),
         Sex.x = coalesce(Sex.x, Sex.y),
         Resting.midpoint = (Resting.x+Resting.y)/2, 
         Max.midpoint = (Max.x+Max.y)/2, 
         AAS.midpoint = (AAS.x+AAS.y)/2)

Juveniles

df_jresp$Population <-  fct_collapse(df_jresp$Population, 
                                      `Vlassof cay`= c("Vlassof reef", "Vlassof", "Vlassof Cay", "Vlassof cay"), 
                                      `Arlington reef` = c("Arlington reef","Arlginton reef")) 

df_jresp$Female <-  fct_collapse(df_jresp$Female, 
                                  `CARL359`= c("CARL359", "CARL59")) 


df_jresp2 <-  df_jresp |> 
  unite("F0", c("Male","Female"), sep="_", remove=FALSE) |>
  mutate(across(1:7, factor), 
         Temperature = factor(Temperature), 
         True_resting = factor(True_resting)) 

#df_jresp2_rest <- df_jresp2 |> 
  #filter(True_resting == "Y")

Merging dataframes

temp1a <- df_jresp2 |> 
  mutate(FISH_ID.x = Male)
temp1b <- df_jresp2 |> 
  mutate(FISH_ID.y = Female)
temp2a <- temp1a |> 
  left_join(select(df_adults_cleaned2, c("FISH_ID.x",
                                          "Sex.x",
                                          "Resting.x", 
                                          "Max.x", 
                                          "AAS.x", 
                                          "Mass.x")), 
                    by="FISH_ID.x")
temp2b <- temp1b |> 
  left_join(select(df_adults_cleaned2, c("FISH_ID.y",
                            "Sex.y",
                            "Resting.y", 
                            "Max.y", 
                            "AAS.y", 
                            "Mass.y")), 
                   by="FISH_ID.y") 
df_merged <- temp2a |> 
  left_join(select(temp2b, c("Clutch","Replicate", 
                             "FISH_ID.y",
                             "Resting.y", 
                             "Max.y", 
                             "AAS.y", 
                             "Mass.y")), 
            by=c("Clutch","Replicate"))
df <- df_merged |> 
  mutate(Resting_MALE =Resting.x, 
         Max_MALE =Max.x, 
         AAS_MALE =AAS.x, 
         Mass_MALE =Mass.x, 
         FISH_ID.y =FISH_ID.x,#makes more sense for males to be .y instead of .x
         FISH_ID.x =FISH_ID.x, 
         Resting_FEMALE =Resting.y, 
         Max_FEMALE =Max.y, 
         AAS_FEMALE =AAS.y, 
         Mass_FEMALE =Mass.y) |> 
  mutate(Resting_MID =(Resting_MALE+Resting_FEMALE)/2, 
         Max_MID =(Max_MALE+Max_FEMALE)/2, 
         AAS_MID =(AAS_MALE+AAS_FEMALE)/2) # easier to do it again

Exploratory analysis

Offspring-Male

plot1 <- ggplot(df, aes(x=Resting_MALE, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") + 
  xlab("") + 
  ylab("Resting (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot2 <- ggplot(df, aes(x=Max_MALE, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("") + 
  ylab("Max (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot3 <- ggplot(df, aes(x=AAS_MALE, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("") + 
  ylab("AAS (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot4 <- ggplot(df, aes(x=Resting_MALE, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") + 
  xlab("Resting (offspring)") + 
  ylab("Resting (parental-male)") +
  theme_classic() + 
  theme(legend.position = "bottom")

plot5 <- ggplot(df, aes(x=Max_MALE, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("Max (offspring)") + 
  ylab("Max (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot6 <- ggplot(df, aes(x=AAS_MALE, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-male relationship") +
  xlab("AAS (offspring)") + 
  ylab("AAS (parental-male)") +
  theme_classic() + 
  theme(legend.position = 'none') 

ggarrange(plot1, plot2, plot3, 
          plot4, plot5, plot6,
          ncol = 3, 
          nrow = 3)

Offspring-Female

plot1 <- ggplot(df, aes(x=Resting_FEMALE, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") + 
  xlab("") + 
  ylab("Resting (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot2 <- ggplot(df, aes(x=Max_FEMALE, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") +
  xlab("") + 
  ylab("Max (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot3 <- ggplot(df, aes(x=AAS_FEMALE, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") +
  xlab("") + 
  ylab("AAS (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot4 <- ggplot(df, aes(x=Resting_FEMALE, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") + 
  xlab("Resting (offspring)") + 
  ylab("Resting (parental-female)") +
  theme_classic() + 
  theme(legend.position = "bottom")

plot5 <- ggplot(df, aes(x=Max_FEMALE, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") +
  xlab("Max (offspring)") + 
  ylab("Max (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot6 <- ggplot(df, aes(x=AAS_FEMALE, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-female relationship") +
  xlab("AAS (offspring)") + 
  ylab("AAS (parental-female)") +
  theme_classic() + 
  theme(legend.position = 'none') 

ggarrange(plot1, plot2, plot3, 
          plot4, plot5, plot6,
          ncol = 3, 
          nrow = 3)

Offspring-Midpoint

plot1 <- ggplot(df, aes(x=Resting_MID, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") + 
  xlab("") + 
  ylab("Resting (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot2 <- ggplot(df, aes(x=Max_MID, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  xlab("") + 
  ylab("Max (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot3 <- ggplot(df, aes(x=AAS_MID, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  xlab("") + 
  ylab("AAS (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot4 <- ggplot(df, aes(x=Resting_MID, y=Resting, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") + 
  xlab("Resting (offspring)") + ylab("Resting (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot5 <- ggplot(df, aes(x=Max_MID, y=Max, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  xlab("Max (offspring)") + ylab("Max (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none')

plot6 <- ggplot(df, aes(x=AAS_MID, y=AAS, color=Temperature)) + 
  stat_smooth(method = "lm") +
  #geom_point(alpha=0.1) + 
  ggtitle("Offspring-midpoint relationship") +
  xlab("AAS (offspring)") + ylab("AAS (parental-midpoint)") +
  theme_classic() + 
  theme(legend.position = 'none') 

ggarrange(plot1, plot2, plot3, 
          plot4, plot5, plot6,
          ncol = 3, 
          nrow = 3, 
          common.legend = TRUE)

Descriptive statistics

Juveniles - overview

Overview

tinytable_7chcwvmk810aswv4s5md
Population 27 28.5 30
Arlington reef 60 43 53
Pretty patches 26 21 34
Sudbury reef 27 15 16
Vlassof cay 26 10 28 
datasummary(Factor(F0) ~ Factor(Temperature), 
            data = df, 
            fmt = "%.0f")
tinytable_yltjnor6oqd5ojomkhfl
F0 27 28.5 30
CARL217_CARL226 0 8 0
CARL218_CARL222 0 0 13
CARL230_CARL235 14 0 0
CARL233_CARL215 0 0 8
CARL237_CARL219 10 0 0
CARL241_CARL239 15 0 0
CARL249_CARL360 0 0 16
CARL335_CARL359 0 14 0
CARL338_CARL345 0 8 0
CARL344_CARL370 0 0 16
CARL354_CARL355 21 0 0
CARL367_CARL363 0 7 0
CARL369_CARL349 0 6 0
CPRE189_CPRE202 0 0 15
CPRE372_CPRE209 14 0 0
CPRE375_CPRE377 12 0 0
CPRE391_CPRE390 0 0 6
CPRE447_CPRE452 0 0 13
CPRE453_CPRE459 0 7 0
CPRE521_CPRE524 0 7 0
CPRE550_CPRE533 0 7 0
CSUD002_CSUD213 0 8 0
CSUD009_CSUD212 14 0 0
CSUD013_CSUD017 13 0 0
CSUD016_CSUD078 0 7 0
CSUD312_CSUD304 0 0 16
CVLA089_CVLA059 0 0 7
CVLA098_CVLA049 0 10 0
CVLA102_CVLA466 6 0 0
CVLA106_CVLA091 0 0 15
CVLA468_CVLA477 13 0 0
CVLA486_CVLA463 7 0 0
CVLA498_CVLA493 0 0 6

Juveniles

Resting oxygen uptake

tinytable_xr0dj0umx5thhu0oanzt
Temperature NUnique mean median min max sd Histogram
27 135 0.21 0.21 0.08 0.64 0.07 ▃▆▇▅▁▁
28.5 89 0.23 0.23 0.09 0.47 0.08 ▂▄▆▆▇▄▁▁ ▁
30 131 0.23 0.23 0.06 0.40 0.07 ▁▂▃▆▇▅▆▄▁▁

Maximum oxygen uptake

tinytable_yv88hrtaag6la1eeg5en
Temperature NUnique mean median min max sd Histogram
27 132 0.58 0.55 0.27 1.66 0.19 ▄▇▆▃▁
28.5 85 0.65 0.64 0.24 1.08 0.18 ▂▄▇▇▇▃▃▂▂
30 130 0.65 0.64 0.16 1.29 0.19 ▂▃▇▅▆▃▁

Absolute aerobic scope

tinytable_rxgj8wyjt69gq0og79xt
Temperature NUnique mean median min max sd Histogram
27 128 0.37 0.34 0.14 1.02 0.14 ▃▇▇▄▃▂
28.5 85 0.42 0.39 0.10 0.79 0.15 ▁▃▅▇▄▃▅▃▁▁
30 130 0.42 0.41 0.09 0.99 0.15 ▁▄▆▅▇▃▁

Adults - overview

Overview

datasummary(Factor(Population) ~ Factor(Temperature), 
            data = df_adults_cleaned, 
            fmt = "%.0f")
tinytable_0s3fznmoj2nflev21c0n
Population 27 28.5 30
Arlington reef 8 7 4
Pretty patches 4 6 4
Sudbury reef 4 3 2
Vlassof cay 6 2 5 
datasummary(Factor(Population) ~ Factor(Temperature)*Factor(Sex), 
            data = df_adults_cleaned, 
            fmt = "%.0f")
tinytable_f2h3v91ssusezw6xhxik
27 28.5 30
Population F M F M F M
Arlington reef 4 4 2 5 2 2
Pretty patches 2 2 3 3 3 1
Sudbury reef 2 2 1 2 1 1
Vlassof cay 3 3 1 1 3 2

Pairs

datasummary(Factor(Population)*Factor(Temperature.x) ~ AAS.midpoint*(NUnique), 
            data = df_adults_cleaned2, 
            fmt = "%.0f")
tinytable_ux9qgpxngjjbqtbhd8gw
Population Temperature.x NUnique
Arlington reef 27 3
28.5 2
30 2
Pretty patches 27 2
28.5 3
30 1
Sudbury reef 27 2
28.5 2
30 1
Vlassof cay 27 3
28.5 1
30 2

Adults

Resting oxygen uptake

tinytable_n67i6zke3ohl40m8yvhu
Temperature NUnique mean median min max sd Histogram
27 22 6.29 6.06 3.82 10.09 1.56 ▂▂▃▇▂▂▁▁▁▁
28.5 18 6.49 6.96 4.35 8.49 1.45 ▇▂▅▂▃▃▅▃
30 15 7.29 7.20 5.14 9.15 1.46 ▅▂▇▂▂▂▇▇

Maximum oxygen uptake

tinytable_iiwz46gzou1vobdpl1b9
Temperature NUnique mean median min max sd Histogram
27 22 16.58 16.91 9.70 22.06 3.36 ▃▃▅▅▃▃▅▇▂
28.5 18 17.09 17.23 11.04 28.39 3.94 ▅▂▅▇▇▃▂
30 15 16.48 16.83 11.78 21.24 2.82 ▂▃▂▃▇▂▂▃▂

Absolute aerobic scope

tinytable_gisw6et1art0kzaoixk3
Temperature NUnique mean median min max sd Histogram
27 22 10.29 10.26 3.85 16.28 3.14 ▃▁▄▇▃▆▃▃▁
28.5 18 10.59 9.66 6.11 20.44 3.66 ▅▅▇▇▃▂▂
30 15 9.19 9.16 4.36 12.77 2.91 ▃▂▅▂▂▂▃▇

Relationships

Offspring-Male

Fit model [random factors]

Models

model1 <- glmmTMB(Resting ~ (1|Clutch), 
                  family="gaussian",
                  data = df) 

model2 <- glmmTMB(Resting ~ (1|Clutch) + (1|Population), 
                  family="gaussian",
                  data = df) 

model3 <- glmmTMB(Resting ~ (1|Clutch) + (1|Chamber), 
                  family="gaussian",
                  data = df) 

model4 <- glmmTMB(Resting ~ (1|Clutch) + (1|Population) + (1|Chamber), 
                  family="gaussian",
                  data = df)

Model selection

AIC(model1, model2, model3, model4, k=2)
BIC(model1, model2, model3, model4)

Model1 performs the best therefore only Clutch will be used as a random factor in future models

Fit model [fixed factors]

After figuring out which random factors will be incorporated into the model we will start to examine out fixed factors. Some fixed factors such as Resting_(FE)MALE and TEMPERATURE will be essential to answering questions we have around heritability. Another factor that will be included is Dry_mass - which it should be pointed out in this experiment refers to the mass of fish after they were blotted dry with paper towel rather than completely dried out. Larger fish consume more oxygen, therefore, we need to account for this known relationship within our model. Out model will look something like this:

Resting ~ Resting_MALE*Temprature + scale(Dry_mass)

If we had alternative hypotheses to test would would do so at this stage. But in this instance the experiment was designed to answer a specific question via limiting potential covariates.

model1.1 <- glmmTMB(Resting ~ Resting_MALE*Temperature+scale(Dry_mass) + (1|Clutch), 
                    family="gaussian", 
                    data=df)

Great now lets check how out model performed via model validation techniques

Model validation

To check out model performance we will be using two different packages that perform model diagnositics. The packages used here are just examples, there are other packages out there that can provide the same function.

DHARMa

model1.1 |> 
  simulateResiduals(plot=TRUE) 

## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help. 
##  
## Scaled residual values: 0.148 0.276 0.048 0.008 0.424 0.48 0.14 0.364 0.48 0.216 0.28 0.136 0.288 0.052 0.136 0.112 0.424 0.524 0.092 0.04 ...
model1.1 |> 
  testResiduals(plot=TRUE)

## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.040686, p-value = 0.6975
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0047, p-value = 0.992
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 2, observations = 303, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.0008003725 0.0236391643
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                             0.00660066
## $uniformity
## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  simulationOutput$scaledResiduals
## D = 0.040686, p-value = 0.6975
## alternative hypothesis: two-sided
## 
## 
## $dispersion
## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 1.0047, p-value = 0.992
## alternative hypothesis: two.sided
## 
## 
## $outliers
## 
##  DHARMa outlier test based on exact binomial test with approximate
##  expectations
## 
## data:  simulationOutput
## outliers at both margin(s) = 2, observations = 303, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
##  0.0008003725 0.0236391643
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 ) 
##                                             0.00660066

performance

model1.1 |> check_model(detrend=FALSE)
## `check_outliers()` does not yet support models of class `glmmTMB`.

Partial effect plots

model1.1 |> ggemmeans(~Resting_MALE|Temperature) |> 
  plot(add.data =FALSE)

Model investigations

summary

model1.1 |> summary()
##  Family: gaussian  ( identity )
## Formula:          
## Resting ~ Resting_MALE * Temperature + scale(Dry_mass) + (1 |      Clutch)
## Data: df
## 
##      AIC      BIC   logLik deviance df.resid 
##   -942.0   -908.5    480.0   -960.0      294 
## 
## Random effects:
## 
## Conditional model:
##  Groups   Name        Variance  Std.Dev.
##  Clutch   (Intercept) 0.0004794 0.02190 
##  Residual             0.0021525 0.04639 
## Number of obs: 303, groups:  Clutch, 45
## 
## Dispersion estimate for gaussian family (sigma^2): 0.00215 
## 
## Conditional model:
##                               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                   0.189813   0.025443   7.460 8.63e-14 ***
## Resting_MALE                  0.003188   0.003853   0.827    0.408    
## Temperature28.5              -0.006513   0.045948  -0.142    0.887    
## Temperature30                 0.103654   0.049952   2.075    0.038 *  
## scale(Dry_mass)               0.048960   0.003202  15.290  < 2e-16 ***
## Resting_MALE:Temperature28.5  0.003369   0.007313   0.461    0.645    
## Resting_MALE:Temperature30   -0.010211   0.007444  -1.372    0.170    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ANOVA

model1.1 |> Anova()

confint

model1.1 |> confint()
##                                     2.5 %      97.5 %     Estimate
## (Intercept)                   0.139945198 0.239680024  0.189812611
## Resting_MALE                 -0.004363672 0.010740654  0.003188491
## Temperature28.5              -0.096569126 0.083543914 -0.006512606
## Temperature30                 0.005749589 0.201557639  0.103653614
## scale(Dry_mass)               0.042683965 0.055236062  0.048960013
## Resting_MALE:Temperature28.5 -0.010964925 0.017702957  0.003369016
## Resting_MALE:Temperature30   -0.024799620 0.004378381 -0.010210620
## Std.Dev.(Intercept)|Clutch    0.015283839 0.031368998  0.021896089

r-squared

model1.1 |> r2_nakagawa()
## # R2 for Mixed Models
## 
##   Conditional R2: 0.578
##      Marginal R2: 0.484

Pairwise comparisons

emmeans [Temperature]